
where \(\gamma _k^{-1}\)  can be interpreted as the power of each column in \(\mathbf {X}_l^i\)  and \(\imath _{\gamma }=[-\delta \mathbf {1}_{K};(\delta -1)\mathbf {1}_{K}]\) .
Noting that after integrating the gamma hyper-prior, the marginal distribution of model parameters (REF ) is a Student's \(t\)  distribution, which is strongly peaked at zero and with heavy tails, thus promoting sparsity. Furthermore, the gamma hyper-prior (REF ) is conjugate to the Gaussian prior (REF ). This conjugacy permits the closed-form solution of the variational inference [1]}.
